The Weakness Objection

I'm trying to go over topics that generated interest but got left behind in the dash to talk about miracles. This was one of them. Here it is in some detail.

The weakness objection is aimed at the following thesis:

(Theistic Argument Standard) A good theistic argument (i.e., argument whose conclusion is that God or some god exists) is valid and its premises have been shown to be more probable than not.

As such, the weakness objection threatens all natural theology when pursued with the Theistic Argument Standard. Obviously, one could adopt a different standard for natural theology.

I'm going to address this objection to The Theist (anyone advocating theistic arguments and the theistic argument standard).

1. The Theist asserts that God exists and he believes that God exists. His theistic arguments are supposed to justify these assertions and beliefs.

2. The Theist's theistic arguments are deductive.
[[This assumption is me being charitable to The Theist.  Some theists -- Craig for example -- present their arguments as both deductive and inductive, which is incoherent. If The Theists' arguments are NOT deductive, then the weakness problem is WAY worse.]]

3. When The Theist justifies the premises of his theistic arguments, he uses the Theistic Argument Standard, which is that the premises ought to be more probable than not.

4. We not only have beliefs, but we hold our beliefs to different degrees of strength.
[[I'm calling these CONFIDENCE LEVELS, but there is a huge literature on this topic, and these things are also called CREDENCES, DEGREES OF BELIEF, and SUBJECTIVE PROBABILITIES.]]

5. In order for a person to believe or assert some claim, that person ought to have more than just >50% confidence level (>50% confidence level = more probable than not).

6. AT BEST, if The Theist defends the premises of his theistic arguments to >50% confidence, then the conclusions of the theistic arguments have >50% confidence.
[[It is wrong to think that this principle holds of all deductive arguments. It is easy to prove that deductive arguments do not necessarily preserve >50% confidence. However, some deductive arguments do (not most theistic arguments, but no matter). So I'm again being very charitable to The Theist in granting this assumption.]]

Assume these six points are correct and The Theist's justifications of the premises of his theistic arguments are good ones. Then at best, he has shown that the claim that God exists is more probable than not (>50% confidence). But that isn't enough to show that anyone may believe it or assert it because belief and assertion require a higher level of confidence. Therefore, The Theist's theistic arguments, together with his justifications for their premises, do NOT justify the belief that God exists. At best, they justify that it is more probable than not that God exists. [[I don't think they do even this, but that's a different point.]]
 

Alexander wrote:

So >50% probability that X is true is not enough to justify a belief that X is true? What is enough? Do we need 100%? Presumably not, if I want to be justified in asserting statements like "I live in England".
In general: what is "more than >50%"? It sounds bizarre to me. "More than greater than 50%"... how much more is that, exactly? 

It does sound bizarre, but all it means is that the threshold for belief has to be higher than 50%.

Some people do think we need 100%. Here is a paper that argues exactly that (together with a bit of context-dependence). I don't think we need to be committed to something so strong. However, there are some pretty strong reasons to think that the threshold for belief has to be higher than 80% based on simple examples involving a six-sided die. Basically, if the threshold is only 80% for belief, then you should believe that a six-sided die when rolled isn't going to land on any number at all. That's obviously absurd. So the threshold has to be higher than 80%. As the threshold gets pushed higher, the reasons for pushing it higher are less strong.

Alexander wrote:

On another level, and one that you mention: many philosophers (Feser springs to mind, along with almost everyone who advocates a serious Thomistic argument) would say that not only are the premises "more probable than not", the premises have themselves been argued for beyond reasonable doubt. Whether or not they are correct would rely an examination of their arguments, but any argument that holds to a standard stronger than your "Theistic Argument Standard" can ignore your objection entirely. Since you yourself point this out, this wouldn't be a huge problem, but I expect most people on this forum would subscribe to the stronger standard, as classical theists generally do.

Excellent. You're quite right about this. I developed this objection to William Lane Craig in particular, but there are others who advocate the same standard (Mavrodes and Davis). What standards do you think the Classical Theists employ in general? Beyond reasonable doubt seems very high. That means you think anyone who even doubts your claim is irrational (and even more so those that disagree with you). That's pretty hard to come by. I have friends and colleagues who reject the law of non-contradiction (in light of various paradoxes) and adopt various non-classical logics. I've come to think that even these people are not being obviously irrational (although this is a tricky case admittedly). I would be hard pressed to find much in the way of philosophical claims that I take to be beyond a reasonable doubt. Perhaps that's rather idiosyncratic.
 

Alexander wrote:

KevinScharp wrote:

Alexander wrote:

So >50% probability that X is true is not enough to justify a belief that X is true? What is enough? Do we need 100%? Presumably not, if I want to be justified in asserting statements like "I live in England".
In general: what is "more than >50%"? It sounds bizarre to me. "More than greater than 50%"... how much more is that, exactly? 

It does sound bizarre, but all it means is that the threshold for belief has to be higher than 50%.

Some people do think we need 100%. Here is a paper that argues exactly that (together with a bit of context-dependence). I don't think we need to be committed to something so strong. However, there are some pretty strong reasons to think that the threshold for belief has to be higher than 80% based on simple examples involving a six-sided die. Basically, if the threshold is only 80% for belief, then you should believe that a six-sided die when rolled isn't going to land on any number at all. That's obviously absurd. So the threshold has to be higher than 80%. As the threshold gets pushed higher, the reasons for pushing it higher are less strong.

In the case of a six sided die, there is a clear reason for putting the standards where they are. It seems odd that you would claim this can be applied to another belief, without the same reason to do so. If all you mean is "the threshold for belief has to be higher than 50%", as you say here, well, that just is the Theistic Argument Standard.

Where is the threshold for belief? In other words, above what level (the threshold) does a confidence level count as a belief. Maybe it is 80%, as I suggested in the talk.

Here's an argument that it must be greater than 80%.
There's an 83% chance of not rolling a 1. Same for a 2 and 3, 4, 5, 6. So your confidence level for the claim that you're not going to roll a 1 should be 83% (or close because confidence levels need not be that precise). If any confidence level greater than 80% counts as a belief, then you believe that you are not going to roll a 1. Same for a 2 and 3, 4, 5, 6. But that's absurd. So the threshold level for belief has to be higher than 83%. Okay, so I want to make sure the example makes sense. If you agree with the example but you think the threshold should be considerable lower in the case of God's existence, then I'd like to hear some reasons for that. If I've misunderstood your comment (which I feel is likely) then I'm sorry, can you rephrase?

Alexander wrote:

If the premises are more likely than not (i.e. >50%), and the argument is valid, the likelihood of the conclusion being true is greater than 50%. Then again, perhaps I have misunderstood you. Please correct me if so.

I know this seems like a plausible principle, but it's false. It is true that for a valid argument, if the premises are 100%, then the conclusion is 100%. But it doesn't hold in general for any lower confidence level. Interestingly, one can classify valid arguments by how well they "transmit" probability from their premises to their conclusions. Adams has a nice paper on the topic. It might be insightful to classify common theistic arguments into Adams' four types. That would be significant and novel work (probably publishable) as far as I know.

Alexander wrote:

KevinScharp wrote:

Alexander wrote:

On another level, and one that you mention: many philosophers (Feser springs to mind, along with almost everyone who advocates a serious Thomistic argument) would say that not only are the premises "more probable than not", the premises have themselves been argued for beyond reasonable doubt. Whether or not they are correct would rely an examination of their arguments, but any argument that holds to a standard stronger than your "Theistic Argument Standard" can ignore your objection entirely. Since you yourself point this out, this wouldn't be a huge problem, but I expect most people on this forum would subscribe to the stronger standard, as classical theists generally do.

Excellent. You're quite right about this. I developed this objection to William Lane Craig in particular, but there are others who advocate the same standard (Mavrodes and Davis). What standards do you think the Classical Theists employ in general? Beyond reasonable doubt seems very high. That means you think anyone who even doubts your claim is irrational (and even more so those that disagree with you). That's pretty hard to come by. I have friends and colleagues who reject the law of non-contradiction (in light of various paradoxes) and adopt various non-classical logics. I've come to think that even these people are not being obviously irrational (although this is a tricky case admittedly). I would be hard pressed to find much in the way of philosophical claims that I take to be beyond a reasonable doubt. Perhaps that's rather idiosyncratic.
 

If you think someone denying the law of non-contradiction isn't being obviously irrational, then no argument could be beyond reasonable doubt in your eyes, because most (if not all) arguments would be undone if the law of non-contradiction is false. But I would say you are obviously wrong in thinking this.  

Not so. To talk about this, I need to be a bit less sloppy than I was being. The main issue here is what follows from a contradiction, not whether any contradictions are true. In classical logic and lots of other logics, every claim follows from a contradiction. This rule is called ex falso, but it has come to be called explosion recently. There are lots of logics that reject explosion, and in these logics, you can reason with contradictions without them "blowing up" the system. LP is one example, but all the relevance logics like R or E have this feature as well. And there are strong reasons to adopt a relevance logic that are totally independent of the semantic paradoxes. In these logics without explosion, you can do lots of normal reasoning like conjunction intro and elim, most have modus ponens. They have double negation elimination. Some have disjunctive syllogism and conditional proof (it depends on the proof theory on the latter). So there's a wealth of reasoning that doesn't depend on rejecting contradictions. One important question I have asked in my own work is: can one get by with one of these logics in every way one might want? I've argued that the answer is No.

Alexander wrote:

In any case, by "beyond reasonable doubt" I don't mean "the premises are absolutely self-evident" but rather something like "there is no good reason to doubt the truth of the premises", so that was sloppy on my part. I wouldn't claim classical theism has, or requires, the standards of the pure mathematician or logician (though some classical theists, such as Barry Miller, certainly claimed something like it in their proofs, they are in the minority). 

Okay, I like that suggestion. And I like the appeal to reasons. I'll think it through.

Alexander wrote:

And, if I may be slightly facetious: Denying the law of non-contradiction "in the light of various paradoxes" forces me to imagine someone thinking "I can't solve this paradox, nor can anyone else I know, therefore it can't be solved, in which case the law of non-contradiction must not apply." Which is just lazy.

I used to think the same thing -- I think I called it "desperate" or "heroic" (the latter isn't a compliment in philosophy) in some of my early publications. I did my graduate work on truth and the liar paradox, and published my first book on it (Replacing Truth). You can probably find a copy for free on libgen. Anyway, as I was researching this topic, I started out thinking that dialetheism (the view that some contradictions are true) was crazy. However, I've changed my mind on this as a result of seeing the internal logic of dialetheism (learning to see the world like a dialetheist) and having lots of conversations with Graham Priest, who had defended the view vigorously over the last four decades. His book, In Contradiction, is still a good introduction. Don't get me wrong -- I think dialetheism is totally wrong (a non-dialetheist has to say that it is "just false", otherwise calling it "false" is compatible with it being both true and false, which is what the dialetheist thinks of her own view). I'm just not sure it's irrational to doubt the law of non-contradiction.
 

Last edited by KevinScharp (5/05/2016 9:14 am)

Tomislav Ostojich wrote:

KevinScharp wrote:

Not so. To talk about this, I need to be a bit less sloppy than I was being. The main issue here is what follows from a contradiction, not whether any contradictions are true. In classical logic and lots of other logics, every claim follows from a contradiction. This rule is called ex falso, but it has come to be called explosion recently. There are lots of logics that reject explosion, and in these logics, you can reason with contradictions without them "blowing up" the system. LP is one example, but all the relevance logics like R or E have this feature as well. And there are strong reasons to adopt a relevance logic that are totally independent of the semantic paradoxes. In these logics without explosion, you can do lots of normal reasoning like conjunction intro and elim, most have modus ponens. They have double negation elimination. Some have disjunctive syllogism and conditional proof (it depends on the proof theory on the latter). So there's a wealth of reasoning that doesn't depend on rejecting contradictions. One important question I have asked in my own work is: can one get by with one of these logics in every way one might want? I've argued that the answer is No.

(1) Relevance logic is just modal logic in disguise.
(2) Paraconsistent logics don't actually solve paradox because, counter-intuitively, they're strictly weaker than classical logic. Yes, if I impoverish my system so that I can't talk about certain things, then I will end up with the result that I can't talk about certain things, and some of those things just might be paradoxes, but this isn't because you actually solved the paradox. You just impoverished the system. It's not unlike how psychiatrists treated mood disorders with a lobotomy, observed the patient was not as moody as before, and declared success.

You see, there's actually a reason why philosophers for the past 2,000 years have adopted classical logic: because classical logic (and intuitionistic logic, but as I will shortly demonstrate, this is really just classical logic) has a computational interpretation. Let our language have the connectives {-->, falsum} together with the following axioms:

(1) P -> (Q -> P)
(2) (P -> (Q -> R)) -> ((P -> Q) -> (P -> R))
(3) ((P -> Q) -> P) -> P

Together with

MP: P, P -> Q |- Q

Each part of this system has a computational interpretation.

(*) "P -> Q" corresponds to a computational function from type P to type Q
(*) "falsum" corresponds to a failed computation
(*) The first two axioms correspond to the combinators S and K (if you don't know what these are, look them up)
(*) Pierce's law corresponds to the scheme function call-with-current-continuation
(*) Modus ponens corresponds to function application

This computational interpretation is very useful, because it corresponds to any computation expressible by the universal turing machine. You get rid of classical logic, you get rid of the turing machine. Sorry for raining on your parade.

You don't have the first clue what my parade even is. I advocate classical logic.

Alexander wrote:

KevinScharp wrote:

Where is the threshold for belief? In other words, above what level (the threshold) does a confidence level count as a belief. Maybe it is 80%, as I suggested in the talk.

Here's an argument that it must be greater than 80%.
There's an 83% chance of not rolling a 1. Same for a 2 and 3, 4, 5, 6. So your confidence level for the claim that you're not going to roll a 1 should be 83% (or close because confidence levels need not be that precise). If any confidence level greater than 80% counts as a belief, then you believe that you are not going to roll a 1. Same for a 2 and 3, 4, 5, 6. But that's absurd. So the threshold level for belief has to be higher than 83%. Okay, so I want to make sure the example makes sense. If you agree with the example but you think the threshold should be considerable lower in the case of God's existence, then I'd like to hear some reasons for that. If I've misunderstood your comment (which I feel is likely) then I'm sorry, can you rephrase?

Sure. My point here wasn't that the threshold ought to be lower than 80%, rather that you give no reason why the threshold should be 80% when it comes to God's existence. That threshold works for a six sided die because of the probabilities involved, but unless you can show a relevant similarity in theism, why apply the same standard? Your chance of not rolling a 1 with a 20-sided die is 95% (good news for D&D players!) - why not use this? Or the chance of not rolling a 1 with a 10-sided die? Or the chance of getting heads rather than tails on a coin flip? Why take the question of rolling a six sided die to be at all representative of the question of theism in the first place, when it seems such an arbitrary example?

I like this direction -- it's careful and it has a D&D reference.

I'm not committed to the threshold in the case of theism being 80%. That was just an example. I am committed to it being greater than 51% or anything close to that. You are right that we can use similar examples to push the threshold higher -- examples with more complex dice. It isn't obvious that we can use the method to push it all the way to 100% because as we get close, the vagueness of confidence levels starts to have a big effect. I know you aren't saying we can push it to 100%. I'm just describing the conceptual terrain.

Why think that the dice cases are good models for theism? I wasn't claiming that they are. I think the threshold for belief goes up or down depending on the context. Although it moves around a bit, I don't think it moves very low -- anywhere close to 50%.

One important question that your comment presses is: what determines the threshold in a particular context? There is some evidence to think that it has to do with the space of alternative possibilities taken seriously by the people in question. There is some evidence that it has to do with the interests of the people in question. For example, it might be that when stakes are low (e.g., a Sunday drive) the threshold for belief is lower (e.g., I believe that this road goes through), but when stakes are high (e.g., a trip to the emergency room) the threshold for belief is higher (e.g., I don't believe that the road goes through). I'm not committed to any of these proposals; I'm just illustrating them and emphasizing the need to investigate this topic more if an adequate response to the weakness objection on behalf of the theist is to be forthcoming. I think you've hit on a crucial issue.

Alexander wrote:

KevinScharp wrote:

Alexander wrote:

If the premises are more likely than not (i.e. >50%), and the argument is valid, the likelihood of the conclusion being true is greater than 50%. Then again, perhaps I have misunderstood you. Please correct me if so.

I know this seems like a plausible principle, but it's false. It is true that for a valid argument, if the premises are 100%, then the conclusion is 100%. But it doesn't hold in general for any lower confidence level.

Yes, I did mess up my maths here! A quick calculation in my head revealed as much, so do ignore that point.

KevinScharp wrote:

Alexander wrote:

If you think someone denying the law of non-contradiction isn't being obviously irrational, then no argument could be beyond reasonable doubt in your eyes, because most (if not all) arguments would be undone if the law of non-contradiction is false. But I would say you are obviously wrong in thinking this.  

Not so. To talk about this, I need to be a bit less sloppy than I was being. The main issue here is what follows from a contradiction, not whether any contradictions are true. In classical logic and lots of other logics, every claim follows from a contradiction....So there's a wealth of reasoning that doesn't depend on rejecting contradictions. One important question I have asked in my own work is: can one get by with one of these logics in every way one might want? I've argued that the answer is No.

It looks like I misunderstood you here. No complaints from me, so long as you aren't accepting the possibility of true contradictions. On the other hand, the logicians on this forum may still take issue with these systems of logic - I do not know enough about the topic to begin to response to them, so I'll leave this point.

This is my bread and butter so I'd be happy to talk it through.

Alexander wrote:

A final note: I'm glad you understood what I meant about reasonable doubt, I wasn't sure I'd presented it well.

I found it very clear. I like this proposal in part because I like explaining normative things in terms of reasons. They're super flexible and cover a wide ground. One issue will be the distinction between contributory reasons and conclusive reasons. The contributory reasons are all the considerations in favor or against whatever is being discussed. The conclusive reasons are the ones that end up out weighing or somehow triumphing over the others. Often when people talk about "good" reasons, they mean conclusive reasons. But not always.